Formalisms Course Notes 1

Ash Asudeh University of Canterbury [email protected]

December 6–7, 2004

1 Theoretical

• Linguistics := The study of human language • Linguistic theory := 1. A scientific theory of human languages (Bloomfield) 2. A scientific theory of knowledge of language (Chomsky)

• Pollard and Sag on mathematical theories: In any mathematical theory about an empirical domain, the phenomena of inter- est are modelled by mathematical structures, certain aspects of which are con- ventionally understood as corresponding to observables of the domain. The the- ory itself does not talk directly about the empirical phenomena; instead, it talks about, or is interpreted by, the modelling structures. Thus the predictive power of the theory arises from the conventional correspondence between the model and the emprirical domain. (Pollard and Sag 1994:6)

• Grammar formalism := a mathematically precise notation for formalizing a theory of gram- mar

• Chomsky on the need to formalize linguistic theory: Precisely constructed models for linguistic structure can play an important role, both negative and positive, in the process of discovery itself. By pushing a precise but inadequate formuolation to an unacceptable conlusion, we can often expose the exact source of this inadequacy and, consequently, gain a deeper understand- ing of the linguistic data. More positively, a formalized theory may automatically provide solutions for many problems other than those for which it was explicitly designed. Obscure and intuition-bound notions can neither lead to absurd con- clusions nor provide new and correct ones, and hence they fail to be useful in two important respects. I think that some of those linguists who have questioned the value of precise and technical development of linguistic theory have failed to recognize the productive potential in the method of rigorously stating a proposed theory and applying it strictly to linguistic material with no attempt to avaoid un- acceptable conclusions by ad hoc adjustments or loose formulation. (Chomsky 1957:5)

1 Grammar Formalisms (Asudeh) ALTSS 2004, Sydney Notes.1 / 2

• In grammar engineering and other computational applications of linguistics, we have no choice: a formalism is required for the simple reason that we need a language for encoding that is a) understandable by humans and b) understandable by computers:

◦ Grammar development in machine language is not feasible for humans. ◦ Computers can’t understand natural language statements of grammars, no matter how perspicuous to humans.

• :

(1) a. Colorless green ideas sleep furiously. (Chomsky 1957) b. *Furiously sleep ideas green colorless. (2) a. Revolutionary new idea appear infrequently. (Sells 1985) b. *Infrequently appear ideas new revolutionary.

• := The sub-field in linguistics concerned with how combine into larger units — phrases — and how phrases in turn combine into yet larger units:

◦ order (3) a. Her tall brother is handsome. b. *Tall her is handsome brother. (4) a. Aren’t I allowed to attend? b. *I aren’t allowed to attend. ◦ agreement (5) Every girl / *girls is / *are female / *females. (6) All *girl / girls *is / are female / females. ◦ heads and complementation (7) a. Thora fears the vacuum cleaner. b. Thora fears that the vacuum cleaner will get her. c. *Thora fears of the vacuum cleaner. (8) a. *Thora is afraid the vacuum cleaner. b. Thora is afraid that the vacuum cleaner will get her. c. Thora is afraid of the vacuum cleaner. (9) a. The vacuum cleaner frightens Thora. b. *The vacuum cleaner frightens Thora that it will get her. c. *The vacuum cleaner frightens of Thora. Grammar Formalisms (Asudeh) ALTSS 2004, Sydney Notes.1 / 3

◦ bounded dependencies (10) a. Mary said Ken pinched her. b. *Mary said Ken pinched herself. c. Mary said Ken pinched himself. ◦ (11) a. David said Ken and Mary tried to arrive together. b. *Ken and Mary said David tried to arrive together. ◦ unbounded dependencies (12) What did Kim claim that Sandy suspected that Robin stole? • := The sub-field in linguistics concerned with meaning. ◦ Truth conditions (13) “Snow is white” is true if and only if snow is white. ◦ Entailment (14) Every student wants good grades ⇒ That student wants good grades ◦ Presupposition (15) Jones has stopped smoking presupposes that Jones smoked

1.1 Modern Perspectives • := A system of rules that defines in a formally precise way (i.e. ‘gen- erates’ [in the mathematical sense – AA]) a set of [structures] that represent the well-formed sentences of a given language. (Sag et al. 2003:525) ◦ This only covers syntax, but generative grammar extends to other sub-systems of lin- guistic information (semantics, , ) under the requirement that explicit systems of rules for those sub-systems are stated. • Two conceptions of language (Soames 1984): ◦ Languages are abstract mathematical systems in the world. (mathematical/Platonic conception) ◦ Languages are internalized systems of knowledge in the minds of speakers. (psychological/cognitive conception) • The currently dominant view in linguistics and cognitive science is the second, cogni- tive/”Knowledge of Language” conception (discussed cogently in Chomsky 1986:1–50). ◦ Three basic questions for linguistics (Chomsky 1986:3): 1. What constitutes knowledge of language? 2. How is knowledge of language acquired? 3. How is knowledge of language put to use? ◦ Chomsky’s goals and assumptions (Green and Morgan 2001:2–6): 1. The mind is innately structured. 2. The mind is modular. 3. There is a distinct module for language. 4. is the central puzzle for linguistic theory. 5. Syntax is formal. 6. Knowledge of language is itself modular. Grammar Formalisms (Asudeh) ALTSS 2004, Sydney Notes.1 / 4

1.2 Goalsof the Field • Acquisition and learnability

• Typology and universals

• Explanatory wide coverage

• Human language processing

• Computation linguistics

◦ Mathematical linguistics ◦ ◦ Generation ◦ Statistical NLP

2 Grammatical Architectures

2.1 Categorial Grammar

• Form-meaning pairing (PHONETICFORM–PREDICATE-ARGUMENT STRUCTURE), mediated by syntactic categories, projected from lexicon

LEXICON married := (S\NP)/NP: married 0

Combinatory Projection

Anna married Manny := S: (λx.married 0x anna0) manny0

Phonology Normalization

PHONETIC FORM PREDICATE-ARGUMENT STRUCTURE “Anna married Manny” married 0manny0anna0

2.2 Head-Driven • Sign-based architecture (term sign used in the sense of Saussure 1919/1959)

(16) PHONOLOGY h . . . i   CATEGORY category      SYNSEM CONTENT content         CONTEXT context  sign • Directed acyclic graphs represent sorted feature structures, the objects in the theory that model linguistic phenomena (signs)

• Attribute-value matrices describe feature structures Grammar Formalisms (Asudeh) ALTSS 2004, Sydney Notes.1 / 5

2.3 Lexical Functional Grammar • Parallel projection architecture (Kaplan 1987, Halvorsen and Kaplan 1988, Kaplan 1989)

◦ Separate levels of representation (projections) model different aspects of linguistic information · Constituent structure (c-structure): precedence, dominance, constituency · Functional structure (f-structure): grammatical functions, predication, subcatego- rization, bounded and unbounded dependencies ◦ Each projection modelled by logics and data structures appropriate for capturing the information it models · C-structure: trees, described by phrase structure rules · F-structure: tabular functions (represented as attribute value matrices), described by regular expressions ◦ Projection functions map from projection to successive projection

information structure •

phonological structure • ι morphological structure ρ • µ Form φ Meaning ••π α •λ •••σ ψ string c-structure argument structure f-structure s-structure model

References

Chomsky, Noam. 1957. . The Hague: Mouton.

—. 1986. Knowledge of Language: Its nature, origin, and use. New York: Praeger.

Dalrymple, Mary, Ronald M. Kaplan, John T. Maxwell, and Annie Zaenen, eds. 1995. Formal issues in Lexical-Functional Grammar. Stanford, CA: CSLI Publications.

Green, Geogia M., and Jerry L. Morgan. 2001. A Practical Guide to Syntactic Analysis. Stanford, CA: CSLI Publications, 2nd edn.

Halvorsen, Per-Kristian, and Ronald M. Kaplan. 1988. Projections and Semantic Description in Lexical-Functional Grammar. In Proceedings of the International Conference on Fifth Genera- tion Computer Systems, 1116–1122. Institute for New Generation Systems, Tokyo.

Kaplan, Ronald M. 1987. Three Seductions of Computational . In P. Whitelock, M. M. Wood, H. L. Somers, R. Johnson, and P. Bennett, eds., Linguistic Theory and Computer Applications, 149–181. London: Academic Press. Reprinted in Dalrymple et al. (1995:339– 367).

—. 1989. The Formal Architecture of Lexical-Functional Grammar. In Chu-Ren Huang and Keh- Jiann Chen, eds., Proceedings of ROCLING II, 3–18. Reprinted in Dalrymple et al. (1995:7–27). Grammar Formalisms (Asudeh) ALTSS 2004, Sydney Notes.1 / 6

Pollard, Carl, and Ivan A. Sag. 1994. Head-driven Phrase Structure Grammar. Chicago, IL and Stanford, CA: The University of Chicago Press and CSLI Publications.

Sag, Ivan A., Thomas Wasow, and Emily M. Bender. 2003. Syntactic Theory: A Formal Introduc- tion. Stanford, CA: CSLI Publications, 2nd edn.

Saussure, Ferdinand de. 1919/1959. Course in General Linguistics. New York: McGraw-Hill.

Sells, Peter. 1985. Lectures on Contemporary Syntactic Theory. Stanford, CA: CSLI Publications.

Soames, Scott. 1984. Linguistics and Psychology. Linguistics and Philosophy 7(2): 155–179. Grammar Formalisms ALTSS 2004 Course Notes 2

Ash Asudeh University of Canterbury [email protected]

December 6–7, 2004

1 Syntactic Categories and Basic Combinatorics

• Common syntactic categories:

S sentence, clause (1) [[That the very bouncy ball will bounce on any surface] surprised her]. N noun (2) That the very bouncy [ball] will bounce on any [surface] surprised [her]. NP (3) That [the very bouncy ball] will bounce on [any surface] surprised [her]. V verb (4) That the very bouncy ball will [bounce] on any surface [surprised] her. VP (5) That the very bouncy ball will [bounce on any surface] [surprised her]. P preposition (6) That the very bouncy ball will bounce [on] any surface surprised her. PP prepositional phrase (7) That the very bouncy ball will bounce [on any surface] surprised her. A adjective (8) That the very [bouncy] ball will bounce on any surface surprised her. AP adjective phrase (9) That the [very bouncy] ball will bounce on any surface surprised her.

1 Grammar Formalisms (Asudeh) ALTSS 2004, Sydney Notes.2 / 2

• Functional categories:

I inflection (10) That the very bouncy ball [will] bounce on any surface surprised her. IP inflectional phrase (That the very bouncy ball [will bounce on any surface] [surprised her) ]. C complementizer (11) [That] the very bouncy ball will bounce on any surface surprised her. CP complementizer phrase (12) [That the very bouncy ball will bounce on any surface] surprised her. D determiner (13) That [the] very bouncy ball will bounce on [any] surface surprised [her]. DP determiner phrase (14) That [the very bouncy ball] will bounce on [any surface] surprised [her]. Grammar Formalisms (Asudeh) ALTSS 2004, Sydney Notes.2 / 3

1.1 Categorial Grammar 1.1.1 Categories • Set of basic categories; typically:

S clause N common noun NP noun phrase, proper noun, pronoun

• All other categories are compositionally made up out of basic categories:

(15) Intransitive verb: S|N (16) Transitive verb: (S|N)|N (17) Determiner phrase: NP|N (18) Adjective: N|N

1.1.2 Combinatorics • (Functional) application:

◦ Non-directional (result|argument): A|B,B → A ◦ Directional · Forward application (result/argument): A/BB → A · Backward application, “Lambek style”, “result on top” (argument\result): BB\A → A · Backward application, “Steedman style”, “leading edge” (result\argument): BA\B → A

1.1.3 Example

(19) Kim ate the banana NP (S\NP)/NP NP/N N > NP > S\NP < S Grammar Formalisms (Asudeh) ALTSS 2004, Sydney Notes.2 / 4

1.2 Head-Driven Phrase Structure Grammar 1.2.1 Categories • Basic type category introduces the following feature declaration (Pollard and Sag 1994:398):

HEAD head category: "SUBCAT list(synsem)# • Subtypes of head add further feature declarations as appropriate (Pollard and Sag 1994:396–398): head

functional

SPEC synsem h i determiner complementizer substantive

PRD boolean "MOD mod-synsem#

noun verb preposition adjective

CASE case VFORM vform PFORM pform h i AUX boolean h i INV boolean     Grammar Formalisms (Asudeh) ALTSS 2004, Sydney Notes.2 / 5

1.2.2 Combinatorics • Combinations of syntactic units into larger phrases is governed by a number of independent principles and Immediate Dominance Schemas/Rules.

• Key principles:

(20) Head Feature Principle (HFP) In any headed phrase, the HEAD value of the mother and the HEAD value of the head daughter must be identical. (21) Principle (Pollard and Sag 1994) In any headed phrase, the list value of DAUGHTERS | HEAD-DAUGHTER ... SUBCAT is the concatenation of the list value of the phrase’s SUBCAT with the list consist- ing of the SYNSEM values (in order) of the elements of the list value of DAUGHTERS | COMPLEMENT-DAUGHTERS.

SYNSEM ... SUBCAT 1  HEAD-DTR ... SUBCAT 1 ⊕ 2  DAUGHTERS  COMP-DTRS ... SUBCAT 2   " # phrase head-struc    (22) Valence Principle (Sag et al. 2003:106) Unless the rule says otherwise, the mother’s values for the features SPR and COMPS are identical to those of the head daughter. (23) Immediate Dominance Principle Every headed phrase must satisfy exactly one of the ID schemata.

• ID schemas/rules for subjects/specifiers1 and complements

◦ Note: More recent versions of HPSG tend to break SUBCAT up into two lists: SUBJ or SPR and COMPS, where the old SUBCAT is equivalent to SUBJ ⊕ COMPS.

(24) Head- schema (Pollard and Sag 1994:402) The SUBCAT value is the empty list h i, and the DAUGHTERS value is an ob- ject of sort head-comp-struc whose HEAD-DAUGHTER value is a phrase whose COMPLEMENT-DAUGHTERS value is a list of length one. (25) Head-specifier rule (adapted from Sag et al. 2003:501)

phrase SPR h 1 i → 1 H "SPR h i# "COMPS h i #

(26) Head-complement schema (Pollard and Sag 1994:402) The SUBCAT value is a list of length one, and the DAUGHTERS value is an of sort head-comp-struc whose HEAD-DAUGHTER value is a word. (27) Head-complement rule (adapted from Sag et al. 2003:502) phrase word → H 1 ... n "COMPS h i# "COMPS h 1 . . . n i#

1In some versions of HPSG and related formalisms, there is no longer a strong distinction made between subjects and specifiers like determiners or the possessive in John’s destruction of the cake alarmed me. Grammar Formalisms (Asudeh) ALTSS 2004, Sydney Notes.2 / 6

1.2.3 Example (28) Version/style: Pollard and Sag (1994) phrase PHONOLOGY h kim, ate, the, banana i   HEAD 2  SYNSEM | LOCAL | CATEGORY     "SUBCAT h i#       head-comp-struc        phrase        PHON h ate, the, banana i           HEAD 2    LOC | CAT     SUBCAT h 1 i     " #             head-comp-struc              word          PHON h ate i            HEAD-DTR      HEAD 2             CATEGORY        "SUBCAT h 1 , 3 i#                           phrase                PHON h the, banana i              HEAD-DTR    HEAD 6       SYNSEM 3 LOC | CAT                 "SUBCAT h i#          DTRS           DTRS   head-comp-struc                       word                      PHON h banana i      COMP DTRS       -  HEAD-DTR        *  +        HEAD 6 noun        SYNSEM LOC | CAT            5            "SUBCAT h i #       DTRS                                 word                         PHON h the i                 COMP-DTRS         * HEAD det +        SYNSEM 5 LOC | CAT                      "SUBCAT h i#                                                word          PHON h kim i    COMP-DTRS         * HEAD noun +    SYNSEM 1 LOCAL | CATEGORY      SUBCAT      " h i #                   Grammar Formalisms (Asudeh) ALTSS 2004, Sydney Notes.2 / 7

(29) Version/style: Sag et al. (2003)

phrase HEAD 2  SPR h i   COMPS h i     word phrase HEAD noun HEAD 2 1    1 SPR h i  SPR h i     COMPS h i  COMPS h i          Kim word phrase HEAD 2 verb HEAD 6   3  1 SPR h i  SPR h i     COMPS h 3 i  COMPS h i         ate word word HEAD determiner HEAD 6 noun 5    5 SPR h i  SPR h i      COMPS h i  COMPS h i          the banana Grammar Formalisms (Asudeh) ALTSS 2004, Sydney Notes.2 / 8

1.3 Lexical Functional Grammar 1.3.1 Categories • Basic categories

◦ Lexical categories: V0,N0,A0,P0 (often written without the superscript zero) ◦ Functional categories: D0, I0,C0

• Formation of larger categories governed by X-bar theory (Chomsky 1970, Jackendoff 1977): XP

YP X0

X0 ZP

1.3.2 Combinatorics • Annotated phrase structure rules license larger structures:

(30) IP −→ DP I0 DP −→ D0 (↑ SUBJ) = ↓ ↑ = ↓ ↑ = ↓

I0 −→ I VP D0 −→ D NP ↑ = ↓ ↑ = ↓ ↑ = ↓ ↑ = ↓

VP −→ V0 NP −→ N0 ↑ = ↓ ↑ = ↓

V0 −→ V DP N0 −→ N ↑ = ↓ (↑ OBJ) = ↓ ↑ = ↓ • All phrase structure elements are optional and are present only if they dominate lexical material or are required by independent principles of the theory.

• The phrase structure rules license constituent-structure (c-structure) trees that are mapped to attribute-value matrices called functional-structures (f-structures) via the annotations.

• Interpretation of metavariables ↑ and ↓ :

↑ := the f-structure corresponding to the mother of the annotated node (“my mother’s f-structure”) ↓ := the f-structure corresponding to the annotated node (“my f-structure”)

• F-structures are functions in the mathematical sense and must satisfy the following condi- tion:

Consistency (a.k.a Uniqueness Condition; this formulation from Dalrymple 2001:39) In a given f-structure a particular attribute may have at most one value. Grammar Formalisms (Asudeh) ALTSS 2004, Sydney Notes.2 / 9

1.3.3 Example

(31) IP

(↑ SUBJ) = ↓ ↑ = ↓ NP I0

PRED ‘ateh(SUBJ),(OBJ)i’ = ↑ ↓ ↑ = ↓ SUBJ PRED ‘Kim’  N VP  h i  OBJ PRED ‘banana’    Kim ↑ = ↓ (↑ OBJ) = ↓  h i  V DP

ate ↑ = ↓ D0

↑ = ↓ ↑ = ↓ D NP

the ↑ = ↓ N

banana Grammar Formalisms (Asudeh) ALTSS 2004, Sydney Notes.2 / 10

2 Exercises

1. Consider the following sentence:

(1) Kim gave Sandy the banana.

i. Do a Categorial Grammar analysis of this sentence using the Steedman notation. a. What new lexical category do you have to assume? ii. Do an HPSG analysis using the Sag, Wasow, and Bender notation. a. Did you have to make any adjustments to the grammar sketched above? iii. Do an LFG analysis. a. Did you have to make any adjustments to the grammar sketched above? b. Did any issues arise about grammatical functions? If so, how did you deal with them?

2. Consider the following alternation of (1):

(2) Kim gave the banana to Sandy.

i. Do a Categorial Grammar analysis of this sentence using the Steedman notation. a. What new lexical categories do you have to assume? b. Are there any problems/issues with your new lexical items? ii. Do an HPSG analysis using the Sag, Wasow, and Bender notation. a. Did you have to make any adjustments to the grammar sketched above? iii. Do an LFG analysis. a. Did you have to make any adjustments to the grammar sketched above? b. Did any new issues arise about grammatical functions? If so, how did you deal with them? How does it fit with what you did for (1)?

References

Chomsky, Noam. 1970. Remarks on nominalization. In Richard Jacobs and Peter Rosenbaum, eds., Readings in English , 184–221. Waltham, MA: Ginn.

Dalrymple, Mary. 2001. Lexical Functional Grammar. San Diego, CA: Academic Press.

Jackendoff, Ray. 1977. X Syntax: A Study of Phrase Structure. Cambridge, MA: MIT Press.

Pollard, Carl, and Ivan A. Sag. 1994. Head-driven Phrase Structure Grammar. Chicago, IL and Stanford, CA: The University of Chicago Press and CSLI Publications.

Sag, Ivan A., Thomas Wasow, and Emily M. Bender. 2003. Syntactic Theory: A Formal Introduc- tion. Stanford, CA: CSLI Publications, 2nd edn.

Steedman, Mark. 1996. Surface Structure and Interpretation. Cambridge, MA: MIT Press. Grammar Formalisms Course Notes 3

Ash Asudeh University of Canterbury [email protected]

December 6–7, 2004

1 The Role of the Lexicon

1.1 Background • Original generative view of the lexicon (largely abandoned): no rule-governed behaviour in the lexicon; repository of exceptions

• Current, generally accepted view: there are generalizations that need to be encoded lexi- cally; lexicon is structured body of knowledge, not just repository of exceptions

◦ In the majority of current generative theories, the lexicon expresses linguistically sig- nificant generalizations, is highly structured, and delimits combinatoric possibilities to a great extent, through specifications in lexical entries.

• Lexicalist theories, such as CG, HPSG and LFG, have developed increasingly sophisticated views of the lexicon:

◦ Many transformations replaced by lexical rules (some seminal works are Bresnan 1978, Pollard and Sag 1987, Flickinger 1987) ◦ Lexical items assigned rich representations (e.g., Kaplan and Bresnan 1982)‘ ◦ Various methods developed for factoring out common information from lexical items: lexical redundancy rules, type hierarchies, templates/macros ⇒ A lot of modern grammar engineering consists of formulating lexical entries.

1.2 Categorial Grammar • Lexical categories also encode (basic) combinatorics (Bar-Hillel 1953, Lambek 1958). This idea has also been adapted in HPSG (SUBCAT lists) and LFG (PRED features and Complete- ness and Coherence; see below).

• In Combinatory Categorial Grammar (Steedman 2000 is a recent overview), grammars are supplemented with combinators (you can think of these as analogous to schemas/rules) that add further combinatoric possibilities beyond purely lexically-specified ones.

1 Grammar Formalisms (Asudeh) ALTSS 2004, Sydney Notes.3 / 2

1.3 Head-Driven Phrase Structure Grammar • Type-hierarchies (Pollard and Sag 1987, Flickinger 1987) lexeme infl-lxm const-lxm

cn-lxm pn-lxm pron-lxm comp-lxm cntn-lxm massn-lxm verb-lxm

siv-lxm ... srv-lxm adj-lxm adv-lxm det-lxm ... ic-srv-lxm auxv-lxm tv-lxm

stv-lxm dtv-lxm ptv-lxm orv-lxm ocv-lxm (part of type hierarchy in Sag et al. 2003:492)

• Lexical rules (Pollard and Sag 1987, Flickinger 1987, Meurers 1999, 2001):

(1) Plural Noun Lexical Rule (adapted from Sag et al. 2003:503) i-rule

INPUT 1 , cn-lxm   D E    OUTPUT FNPLh 1 i, HEAD AGR NUM plural     * " #+   h i    1.4 Lexical Functional Grammar • Templates (Dalrymple et al. to appear) PRESENT = (↑ TENSE)=PRES 3PERSONSUBJ = (↑ SUBJ PERS)=3 SINGSUBJ = (↑ SUBJNUM)=SG 3SG = @(3PERSONSUBJ) = @(SINGSUBJ) PRES3SG = @(PRESENT) = @(3SG) TRANSITIVE(P) = (↑ PRED)=‘Ph(SUBJ),(OBJ)i’ INTRANSITIVE(P) = (↑ PRED)=‘Ph(SUBJ)i’ TRANSITIVE-OR-INTRANSITIVE(P) = { @(TRANSITIVE P) | @(INTRANSITIVE P) } bakes V @(TRANSITIVE-OR-INTRANSITIVE bake) template form @(PRES3SG) bakes V { (↑ PRED)=‘bakeh(SUBJ),(OBJ)i’ | (↑ PRED)=‘bakeh(SUBJ)i’ } realized (↑ SUBJ PERS)=3 form (↑ SUBJNUM)=SG

(2) a. John bakes bread. b. John bakes. Grammar Formalisms (Asudeh) ALTSS 2004, Sydney Notes.3 / 3

2 Heads

• Heads are distinguished lexical items that determine properties of larger phrases in which they occur, such as:

◦ Category; e.g. a head verb together withs its complements forms a verb phrase (VP). ◦ Agreement; e.g. the noun phrase furry dogs is plural, because its head noun is plural. ◦ Complementation; e.g., the verb hand requires two complements (ditransitive), the verb devour requires one complement (transitive), and the verb arrive takes none (in- transitive).

2.1 Categorial Grammar • Categorial grammar does not have a native notion of head, in the sense of theoretically distinguishing a particular element.

• CG categories correspond tightly to functors and arguments (Steedman 1996). Functors can then be derivatively identified as heads. However, this is not completely straightforward in more powerful CGs. For example, type raising changes an argument into a higher-order functor on the functor that would normally apply to the argument. Which is the head? (advanced answer: the functor in the lowest type)

• The head of a sentence can be identified by finding the (verb) category whose leading edge is the final result of the derivation. The head of sentence (19) in course notes.2 is ate.

2.2 Head-Driven Phrase Structure Grammar • The notion of head is unsurprisingly very important to HPSG.

• There is a feature HEAD that directly encodes the notion. The value of HEAD has many subtypes (see course notes.2, p.4).

• The majority of HPSG structures are headed structures. The head value of the entire struc- ture is identified as token-identical to the head value of the head daughter, as we saw in course notes.2 (28).

• It is possible to follow paths of heads from lexical items all the way to the largest phrase/structure that they head by examining the structure-sharing of the HEAD value between mothers and daughters.

2.3 Lexical Functional Grammar • LFG has a native notion of category/c-structure head, determined by X-bar theory (Chom- sky 1970, Jackendoff 1977), and a derivative notion of f-structure head based on the ↑ and ↓ annotations.

• The f-structure head of a phrase is the lexical item that initiates the path of ↑ = ↓ annotations that terminate at the top of the phrase.

• Functional categories in LFG are typically analyzed as co-heads. They bear the ↑ = ↓ annotation and so does their sister. They therefore contribute information to the same f-structure as their sister. Grammar Formalisms (Asudeh) ALTSS 2004, Sydney Notes.3 / 4

3 Agreement

• Subject-verb

(3) Kim eats the banana. (4) *Kim eat the banana. (5) *Kim and Sandy eats the banana. (6) Kim and Sandy eat the banana.

• Determiner/adjective-noun

(7) A cop chased Sandy. (8) *A cops chased Sandy. (9) Two cops chased Kim. (10) *Two cop chased Kim.

3.1 Categorial Grammar • A common method for specifying agreement in CG is by further annotating categories (Bach 1983, Steedman 1996):

(11) eats := (S\NP3S )/NP

• Lack of specification for agreement features is understood as underspecification. The cate- gory for eats states that it requires a third person singular subject, but makes no requirement on its object.

3.1.1 Examples

(12) Kim eats the banana NP3S (S\NP3S )/NP NP/N N > NP > S\NP3S < S

(13) Cockroaches eats the banana NP3P (S\NP3S )/NP NP/N N > NP > S\NP3S FAIL Grammar Formalisms (Asudeh) ALTSS 2004, Sydney Notes.3 / 5

3.2 Head-Driven Phrase Structure Grammar • Agreement captured by stating restriction on category in valence lists:

(14) word PHONOLOGY h eats i     noun          3sing   SPR HEAD   * AGR PER 3rd+              NUM sg                   • Agreeing item must bear features that can unify appropriately.

3.2.1 Example

(15) phrase HEAD 2  SPR h i   COMPS h i     word phrase  noun  HEAD 2  SPR h 1 i HEAD  PERS 3rd    1     AGR  COMPS h i    "NUM sg #              SPR h i    COMPS h i      Kim word HEAD 2 verb     noun      SPR 1HEAD  PERS 3rd    AGR   * +    "NUM sg #                 COMPS h i      eats Grammar Formalisms (Asudeh) ALTSS 2004, Sydney Notes.3 / 6

3.3 Lexical Functional Grammar • Agreement captured at f-structure. F-structure heads specify the agreement features of their arguments:

(16) eats V (↑ SUBJ PERS) = 3 (↑ SUBJNUM) = SG • These specifications will only be satisfiable (due to Consistency) if the agreeing item bears consistent specifications:

(17) Kim N (↑ PERS) = 3 (↑ NUM) = SG

3.3.1 Example

(18) IP

(↑ SUBJ) = ↓ ↑ = ↓ NP I0

PRED ‘ateh(SUBJ),(OBJ)i’ = ↑ ↓ ↑ = ↓  PRED ‘Kim’  N VP SUBJ PERS 3      NUMSG  Kim ↑ = ↓ (↑ OBJ) = ↓     =     (↑ PERS) 3 V DP     OBJ PRED ‘banana’  (↑ NUM) = SG    h i  eats ↑ = ↓ 0 (↑ SUBJ PERS) = 3 D (↑ SUBJNUM) = SG ↑ = ↓ ↑ = ↓ D NP

the ↑ = ↓ N

banana Grammar Formalisms (Asudeh) ALTSS 2004, Sydney Notes.3 / 7

4 Complementation

• Heads select various aspects of their complements:

◦ Number (a.k.a. valency) (19) a. Thora handed Isak the toy. b. *Thora handed Isak. c. *Thora handed the toy. (20) a. Thora devoured the cookie. b. *Thora devoured Isak the cookie. c. *Thora devoured. (21) a. The train arrived. b. *The train arrived the passengers. ◦ Category (22) That Thora slept through the night surprised us. CP subject (23) Thora surprised us. NP subject (24) *Under the bed surprised us. PP subject (25) *To find a leprechaun surprised us. IP subject (26) *Very rare surprised us. AP subject ◦ Grammatical function (27) Thora seemed sleepy. subject, NP (28) Under the bed seemed dusty. subject, PP (29) Very rare seems to be how George likes his steak. subject,AP (30) To find a leprechaun seems incredibly unlikely. subject, IP (31) That Thora slept through the night seemed surprising. , subject, CP ◦ Grammatical features · Mood (32) Thora suspected that Ida had hidden the cookie. declarative (33) *Thora suspected if Ida had hidden the cookie. (34) *Thora enquired that she could have a cookie. interrogative (35) Thora enquired if she could have a cookie.

4.1 Categorial Grammar • Number and category of complements directly encoded in lexical categories.

• Grammatical function typically derived from argument position in predicate-argument struc- ture.

• Grammatical features either captured in semantics (predicate-argument structure) or through feature specifications on categories (similarly to agreement). Grammar Formalisms (Asudeh) ALTSS 2004, Sydney Notes.3 / 8

4.2 Head-Driven Phrase Structure Grammar

• Number of complements encoded on SUBCAT/VALENCE lists.

• Category of complement captured by stating restriction on category in valence lists:

(36) word PHONOLOGY h surprise i    SPR HEAD noun ∨ comp     h i   COMPS HEAD noun         h i  • Grammatical function derived relationaly from position on SUBCAT list, according to oblique- ness hierarchy: subject ≺ direct object ≺ indirect object ≺ oblique ≺ other complements

• Grammatical features selected through valence lists, analogously to agreement and category.

4.3 Lexical Functional Grammar

• Number of complements and their grammatical functions encoded in PRED feature:

devour (↑ PRED) = ‘devourh(SUBJ),(OBJ)i’

• The principle of Completeness and Coherence ensure that the subcategorization require- ments of the predicate are satisfied:

◦ Completeness (adapted from Dalrymple 2001:37 and Kaplan and Bresnan 1982) An f-structure is complete if and only if it contains all the grammatical functions that its predicate governs. ◦ Coherence (adapted from Dalrymple 2001:39 and Kaplan and Bresnan 1982) An f-structure is coherent if and only if all the governable grammatical functions that it contains are governed by a local predicate. ◦ Governable grammatical functions := GFs that can be subcategorized for ◦ A predicate governs a grammatical function iff the grammatical function is mentioned in the predicate’s PRED feature.

• Grammatical features of complement specified through functional equations:

(↑ COMPMOOD) = DECLARATIVE

• Category selected through interplay of grammatical function annotations on c-structure rules and satisfaction of PRED subcategorization requirements (i.e., Completeness and Coher- ence). Grammar Formalisms (Asudeh) ALTSS 2004, Sydney Notes.3 / 9

5 Exercise

1. Consider the following sentence:

(1) Few cats hand people money.

i. Do a Categorial Grammar analysis of this sentence using the Steedman notation. a. Account for all agreement relations and complementation requirements. ii. Do an HPSG analysis using the Sag, Wasow, and Bender notation. a. Account for all agreement relations and complementation requirements b. Did you have to make any adjustments to the grammar developed so far? iii. Do an LFG analysis. a. Account for all agreement relations and complementation requirements b. Did you have to make any adjustments to the grammar developed so far?

References

Bach, Emmon. 1983. On the Relationship between Word-Grammar and Phrase-Grammar. Natural Language and Linguistic Theory 1: 65–89.

Bar-Hillel, Yehoshua. 1953. A quasi-arithmetical notation for syntactic description. Language 29: 47–58.

Bresnan, Joan. 1978. A Realistic Trasnformational Grammar. In Morris Halle, Joan Bresnan, and George A. Miller, eds., Linguistic Theory and Psychological Reality, 1–59. Cambridge, MA: MIT Press.

Chomsky, Noam. 1970. Remarks on nominalization. In Richard Jacobs and Peter Rosenbaum, eds., Readings in English Transformational Grammar, 184–221. Waltham, MA: Ginn.

Dalrymple, Mary. 2001. Lexical Functional Grammar. San Diego, CA: Academic Press.

Dalrymple, Mary, Ronald M. Kaplan, and Tracy Holloway King. to appear. Lexical Structure as Generalizations over Descriptions. In Miriam Butt and Tracy Holloway King, eds., Proceedings of the LFG04 Conference. Stanford, CA: CSLI Publications.

Flickinger, Daniel. 1987. Lexical Rules in the Hierarchical Lexicon. Ph.D. thesis, Stanford Uni- versity.

Jackendoff, Ray. 1977. X Syntax: A Study of Phrase Structure. Cambridge, MA: MIT Press.

Kaplan, Ronald M., and Joan Bresnan. 1982. Lexical-Functional Grammar: A for Grammatical Representation. In Joan Bresnan, ed., The Mental Representation of Grammatical Relations, 173–281. Cambridge, MA: MIT Press.

Lambek, Joachim. 1958. The Mathematics of Sentence Structure. American Mathematical Monthly 65(154–70).

Meurers, Walt Detmar. 1999. Lexical Generalizations in the Syntax of German Non-Finite Con- structions. Ph.D. thesis, Universit¨at T¨ubingen, T¨ubingen, Germany. Volume 145 in Arbeitspa- piere des SFB 340. Grammar Formalisms (Asudeh) ALTSS 2004, Sydney Notes.3 / 10

—. 2001. On expressing lexical generalizations in HPSG. Nordic Journal of Linguistics 24(2): 161–217.

Pollard, Carl, and Ivan A. Sag. 1987. Information-Based Syntax and Semantics. CSLI Publica- tions.

Sag, Ivan A., Thomas Wasow, and Emily M. Bender. 2003. Syntactic Theory: A Formal Introduc- tion. Stanford, CA: CSLI Publications, 2nd edn.

Steedman, Mark. 1996. Surface Structure and Interpretation. Cambridge, MA: MIT Press.

—. 2000. Information Structure and the Syntax-Phonology Interface. Linguistic Inquiry 31(4). Grammar Formalisms ALTSS 2004 Course Notes 4

Ash Asudeh University of Canterbury [email protected]

December 6–7, 2004

1 Modifiers

• Some common modifiers:

◦ Adjectives (1) a red car (2) an American car (3) a big cockroach (4) a former senator ◦ Adverbs (5) a really big cockroach (6) She foxtrots fabulously. (7) She foxtrots daily. (8) John quickly hid the evidence. (9) Obviously, he is nuts. ◦ Prepositional phrases (10) He arrived on the train. (11) He arrived at the train station. (12) He arrived in one hour. (13) He rode the train for one hour. (14) Is that the man from France? ◦ Noun phrases (15) She foxtrots every day. (16) She does not foxtrot here. ◦ Relative clauses1 (17) Surgeons who are talented deserve awards. (18) Surgeons, who are talented, deserve awards.

1Relative clauses present the added complication of containing an unbounded dependency: (i) The surgeons who the Guardian reported that the Lancet declared are talented deserve awards. We will not account for this complication here.

1 Grammar Formalisms (Asudeh) ALTSS 2004, Sydney Notes.4 / 2

1.1 Categorial Grammar • Modifiers are of the general form A/AorA\A:

◦ Adjective: N/N ◦ Adverb: (S\NP)|(S\NP), S/S, (N/N)/(N/N) ◦ Prepositional phrase: (S\NP)\(S\NP), N\N

1.1.1 Examples

(19) Kim ate the big yellow banana quickly NP (S\NP)/NP NP/N N/N N/N N (S\NP)|(S\NP) > N > N > NP > S\NP < S\NP < S

(20) Kim quickly ate the big yellow banana NP (S\NP)|(S\NP) (S\NP)/NP NP/N N/N N/N N > N > N > NP > S\NP > S\NP < S Grammar Formalisms (Asudeh) ALTSS 2004, Sydney Notes.4 / 3

1.2 Head-Driven Phrase Structure Grammar • Add another schema/rule:

(21) Head-modifier rule (adapted from Sag et al. 2003)

COMPS h i [phrase] → H 1 COMP h i , "MOD h 1 i# h i

1.2.1 Example

(22) phrase HEAD 2  SPR h i   COMPS h i     word phrase HEAD noun HEAD 2 1    1 SPR h i  SPR h i     COMPS h i  COMPS h i          Kim word phrase HEAD adverb HEAD 2   7  1 SPR h i  SPR h i     COMPS h i  COMPS h i         MOD h 7 i        quickly word phrase HEAD 2 verb HEAD 6   3  1 SPR h i  SPR h i     COMPS h 3 i  COMPS h i         ate word phrase HEAD determiner HEAD 6 5    5 SPR h i  SPR h i     COMPS h i  COMPS h i          the word phrase HEAD adjective HEAD 6   9  5 SPR h i  SPR h i     COMPS h i  COMPS h i         MOD h 9 i        big word word HEAD adjective HEAD 6 noun   8  5 SPR h i  SPR h i      COMPS h i  COMPS h i         MOD h 8 i        yellow banana Grammar Formalisms (Asudeh) ALTSS 2004, Sydney Notes.4 / 4

1.3 Lexical Functional Grammar • Expand our set of c-structure rules to deal with modifiers: IP −→ AdvP IP ↓∈ (↑ ADJ) ↑ = ↓

VP −→ AdvP VP AdvP ↓∈ (↑ ADJ) ↑ = ↓ ↓∈ (↑ ADJ)

N0 −→ AP∗ N0 ↓∈ (↑ ADJ) ↑ = ↓

AP −→ A0 ↑ = ↓

A0 −→ AdvP A0 ↓∈ (↑ ADJ) ↑ = ↓

A0 −→ A ↑ = ↓

AdvP −→ Adv0 ↑ = ↓

Adv0 −→ Adv ↑ = ↓

• A new kind of grammatical function at f-structure, ADJUNCT (abbreviated as ADJ):

◦ ADJ has a set as a value. The set contains all of the item’s modifiers, in a flat, unordered representation. ◦ The annotation ↓∈ (↑ ADJ) means that the f-structure of the node bearing the annota- tion is a member of the adjunct set of the mother’s f-structure. ◦ Completeness and Coherence do not apply to ADJ, because it is not a subcatego- rized/governable grammatical function. Grammar Formalisms (Asudeh) ALTSS 2004, Sydney Notes.4 / 5

1.3.1 Example

(23) IP

(↑ SUBJ) = ↓ ↑ = ↓ NP I0

= ↑ ↓ ↑ = ↓ N VP

Kim ↓∈ (↑ ADJ) ↑ = ↓ AdvP VP

↑ = ↓ ↑ = ↓ (↑ OBJ) = ↓ Adv V DP

quickly ate ↑ = ↓ D0

↑ = ↓ ↑ = ↓ D NP

the ↑ = ↓ N0

↓∈ (↑ ADJ) ↓∈ (↑ ADJ) ↑ = ↓ AP AP N0

↑ = ↓ ↑ = ↓ ↑ = ↓ A A N

big yellow banana

PRED ‘ateh(SUBJ),(OBJ)i’ SUBJ PRED ‘Kim’   h i   PRED ‘banana’    OBJ   ADJ PRED ‘big’ , PRED ‘yellow’          h i h i     ADJ PRED ‘quickly’         h i  Grammar Formalisms (Asudeh) ALTSS 2004, Sydney Notes.4 / 6

2 Exercises

1. Consider the following sentence:

(1) Kim ate the very big banana.

i. Do a Categorial Grammar analysis of this sentence using the Steedman notation. a. What new lexical category do you have to assume? ii. Do an HPSG analysis using the Sag, Wasow, and Bender notation. a. Did you have to make any adjustments to the grammar developed so far? iii. Do an LFG analysis. a. Did you have to make any adjustments to the grammar developed so far?

2. Consider the following sentence:

(2) Kim ate the banana on the train.

i. Do a Categorial Grammar analysis of this sentence using the Steedman notation. a. What new lexical category do you have to assume? b. Does this category bear any relationship to any of the lexical categories you had to develop for course notes.2, exercise 2? If so, describe the relationship. ii. Do an HPSG analysis using the Sag, Wasow, and Bender notation. a. Did you have to make any adjustments to the grammar developed so far? iii. Do an LFG analysis. a. Did you have to make any adjustments to the grammar developed so far? iv. Is the sentence ambiguous? If it is, can you account for both parses in each framework (CG, HPSG, LFG)?

References

Sag, Ivan A., Thomas Wasow, and Emily M. Bender. 2003. Syntactic Theory: A Formal Introduc- tion. Stanford, CA: CSLI Publications, 2nd edn.

Steedman, Mark. 1996. Surface Structure and Interpretation. Cambridge, MA: MIT Press. Grammar Formalisms ALTSS 2004 Course Notes 5

Ash Asudeh University of Canterbury [email protected]

December 6–7, 2004

1 Grammar Engineering

1.1 Categorial Grammar • Grok

Comments grammar implementation platform, final release 24/02/2003 License GNU Library or Lesser General Public License (LGPL) Availability downloadable URL http://grok.sourceforge.net/

1.2 HPSG • Linguistic Knowledge Building (LKB; Copestake 2002)

Comments state-of-the-art, grammar and lexicon development environment License Open Source Availability downloadable URL http://www.delph-in.net/lkb/ (also see http://cslipublications.stanford.edu/lkb.html; contains some useful links)

• ALE (Attribute Logic Engine)

Comments grammar implementation platform for typed-feature structure grammars, espe- cially HPSG; semi-maintained (no major versions since 1999) License GNU Lesser General Public License Availability downloadable URL http://www.cs.toronto.edu/∼gpenn/ale.html

1 Grammar Formalisms (Asudeh) ALTSS 2004, Sydney Notes.5 / 2

• TRALE

Comments grammar-implementation platform based on ALE and ConTroll; not publicly available yet License ? Availability contact developers for project-internal release (see web site) URL http://www.sfs.uni-tuebingen.de/hpsg/archive/projects/trale/

• ConTroll

Comments legacy project (finished 1997, principal results incorporated in TRALE); im- plements logical foundations of HPSG; no parser License free to “people and institutions which make all their research results public” Availability downloadable Prolog source code URL http://www.sfs.uni-tuebingen.de/controll/

• See Copestake 2002:156–157 for more references to systems for HPSG and other frame- works.

1.3 LFG • Xerox Linguistics Environment (XLE; Butt et al. 1999)

Comments state-of-the-art, grammar and lexicon development environment License free for education Availability downloadable with username/password after license paperwork has been filed URL http://www2.parc.com/istl/groups/nltt/xle/

• Grammar Writer’s Workbench (a.k.a Medley)

Comments legacy system (replaced by XLE), semi-maintained, development environment License free for research and education Availability downloadable URL http://www2.parc.com/istl/groups/nltt/medley/

References

Butt, Miriam, Tracy Holloway King, Mar´ıa-Eugenia Ni˜no, and Fr´ed´erique Segond. 1999. A Gram- mar Writer's Cookbook. Stanford, CA: CSLI Publications.

Copestake, Ann. 2002. Implementing Typed Feature Structure Grammars. Stanford, CA: CSLI Publications. Grammar Formalisms Selected References

Ash Asudeh University of Canterbury [email protected]

December 6–7, 2004

Note: These references are not meant to be exhaustive in any way. They are rather meant to serve as useful starting points (mainly books) for finding out more information.

Foundations of Generative Linguistics

Chomsky, Noam. 1957. Syntactic Structures. The Hague: Mouton. —. 1965. Aspects of the Theory of Syntax. MIT Press. —. 1970. Remarks on nominalization. In Richard Jacobs and Peter Rosenbaum, eds., Readings in English Transformational Grammar, 184–221. Waltham, MA: Ginn.

Grammar Formalisms

Green, Geogia M., and Jerry L. Morgan. 2001. A Practical Guide to Syntactic Analysis. Stanford, CA: CSLI Publications, 2nd edn. Sells, Peter. 1985. Lectures on Contemporary Syntactic Theory. Stanford, CA: CSLI Publications. Shieber, Stuart M. 1986. An introduction to unification-based approaches to grammar. Stanford, CA: CSLI Publications.

Grammar Engineering

Butt, Miriam, Tracy Holloway King, Mar´ıa-Eugenia Ni˜no, and Fr´ed´erique Segond. 1999. A Grammar Writer’s Cookbook. Stanford, CA: CSLI Publications. Copestake, Ann. 2002. Implementing Typed Feature Structure Grammars. Stanford, CA: CSLI Publica- tions.

Categorial Grammar Introductory Wood, Mary McGee. 1993. Categorial Grammars. London: Routledge.

Foundational Bar-Hillel, Yehoshua. 1953. A quasi-arithmetical notation for syntactic description. Language 29: 47–58. Lambek, Joachim. 1958. The Mathematics of Sentence Structure. American Mathematical Monthly 65(154–70).

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Further Developments van Benthem, Johan. 1991. Language in Action: Categories, Lambdas, and Dynamic Logic. Amsterdam: North-Holland. Reprinted in 1995 by the MIT Press, Cambridge, MA. Buszkowski, Wojciech, Witold Marciszewski, and Johan van Benthem, eds. 1988. Categorial Grammar. Amsterdam: John Benjamins. Carpenter, Bob. 1997. Type-Logical Semantics. Cambridge, MA: MIT Press. Moortgat, Michael. 1997. Categorial type logics. In Johan van Benthem and Alice ter Meulen, eds., Handbook of Logic and Language, 93–177. Cambridge, MA: MIT Press. Co-published with Elsevier Science B.V., Amsterdam, The Netherlands. Morrill, Glyn. 1994. Type Logical Grammar. Dordrecht: Kluwer. Oehrle, Richard T., Emmon Bach, and Deirdre Wheeler, eds. 1988. Categorial Grammars and Natural Language Structures. Dordrecht: Reidel. Steedman, Mark. 1996. Surface Structure and Interpretation. Cambridge, MA: MIT Press. —. 2000. The Syntactic Process. Cambridge, MA: MIT Press.

Head-Driven Phrase Structure Grammar Introductory Sag, Ivan A., Thomas Wasow, and Emily M. Bender. 2003. Syntactic Theory: A Formal Introduction. Stanford, CA: CSLI Publications, 2nd edn. Borsley, Robert D. 1996. Modern Phrase Structure Grammar. Oxford: Blackwell.

Foundational Pollard, Carl, and Ivan A. Sag. 1987. Information-Based Syntax and Semantics. CSLI Publications. —. 1994. Head-driven Phrase Structure Grammar. Chicago, IL and Stanford, CA: The University of Chicago Press and CSLI Publications.

Further Developments Ginzburg, Jonathan, and Ivan Sag. 2001. Interrogative Investigations. Stanford, CA: CSLI Publications. Levine, Robert, and Georgia Green, eds. 1999. Studies in Contemporary Phrase Structure Grammar. Cambridge: Cambridge University Press. Webelhuth, Gert, Jean-Pierre Koenig, and Andreas Kathol, eds. 1999. Lexical and Constructional Aspects of Linguistic Explanation. Stanford, CA: CSLI.

Lexical Functional Grammar Foundational Bresnan, Joan, ed. 1982. The Mental Representation of Grammatical Relations. Cambridge, MA: MIT Press. Dalrymple, Mary, Ronald M. Kaplan, John T. Maxwell, and Annie Zaenen, eds. 1995. Formal issues in Lexical-Functional Grammar. Stanford, CA: CSLI Publications. Grammar Formalisms (Asudeh) ALTSS2004,Sydney SelectedReferences/ 3

Introductory Falk, Yehuda. 2001. Lexical-Functional Grammar: An Introduction to Parallel Constraint-Based Syntax. Stanford, CA: CSLI Publications. Kroeger, Paul. 2004. Analyzing Syntax: A Lexical-Functional Approach. Cambridge: Cambridge Univer- sity Press.

Further Developments Bresnan, Joan. 2000. Optimal Syntax. In Joost Dekkers, Frank van der Leeuw, and Jeroen van de Weijer, eds., Optimality Theory: Phonology, Syntax, and Acquisition, 334–385. Oxford: Oxford University Press.

—. 2001. Lexical-Functional Syntax. Oxford: Blackwell. Dalrymple, Mary, ed. 1999. Semantics and Syntax in Lexical Functional Grammar: The Resource Logic Approach. Cambridge, MA: MIT Press. Dalrymple, Mary. 2001. Lexical Functional Grammar. San Diego, CA: Academic Press. Kuhn, Jonas. 2003. Optimality-Theoretic Syntax: A Declarative Approach. Stanford, CA: CSLI Publica- tions.